We describe a method for solving the joint problem of optimal routing and optimal bandwidth allocation in a network that supports plural subnetworks and plural communication services. Our method involves, for each source-destination pair communicating via a given subnetwork and a given class of service, determining a traffic rate to be offered to each of a set of permissible routes between that source and that destination, in the given subnetwork and service class. Our method further involves allocating a respective bandwidth to each link of each subnetwork. Significantly, the determinations of traffic rate to be offered, and the allocations of bandwidth to respective links of subnetworks, are performed in a mutually responsive manner.